We present three problems motivated by order fulfillment in online retailing. First, we focus on one warehouse or fulfillment center. To optimize the storage space and labor, an e-tailer splits the warehouse into two regions with different storage densities. One is for picking customer orders and the other to hold a reserve stock that replenishes the picking area. Consequently, the warehouse is...

We present three problems motivated by order fulfillment in online retailing. First, we focus on one warehouse or fulfillment center. To optimize the storage space and labor, an e-tailer splits the warehouse into two regions with different storage densities. One is for picking customer orders and the other to hold a reserve stock that replenishes the picking area. Consequently, the warehouse is...

In this paper, we consider inventory models for periodic-review systems with replenishment cycles, which consist of a number of periods. By replenishment cycles, we mean that an order is always placed at the beginning of a cycle. We use dynamic programming to formulate both the backorder and lost-sales models, and propose to charge the holding and shortage costs based on the ending inventory of...

Online purchases constitute about one tenth of US retail sales. The supply chains that support online retailing are fundamentally different from those that support traditional brick-and-mortar stores. Traditional solutions are not always appropriate to solve online retailing’s operations problems; thus, there is an opportunity to understand and improve these novel supply chains. One key charact...

We consider periodic review inventory control problems in directed networks, primary examples of which are distribution systems and assembly systems. External demand could occur at each node. When inventory is insufficient to meet requirements at a node, a portion of this demand is backordered and the remaining is lost. External demands, as well as lead times for inventory purchase, assembly, a...

This article considers five cost-rate models for inventory control, each summarizing the expected holding and shortage costs per period as a function of the inventory position. All models have linear holding costs and shortage cost coefficients of dimension [$/unit/period], [$/unit] and [$/period]. The latter two coefficients may be the shadow costs of a fill-rate and a ready-rate service const...

In this work, optimal control theory is used to derive the optimal production rate in a manu‐ facturing system presenting the following features: the demand rate during a certain period depends on the demand rate of the previous period (dependent demand), the demand rate depends on the inventory level, items in inventory are subject to deterioration, and the firm can adopt a periodic or a conti...

We consider the joint pricing and inventory control problem for a single product whose demand distribution in each period is determined both by whether or not a sale price is offered in the current period, and the number of periods since the last time the sale price was offered. We show that optimal inventory ordering policy is a state dependent base stock policy; however, the optimal pricing p...

to fully implement the principles of humane science, including the unifying concept of the three Rs (Replacement, Reduction, and Refinement of animal use) (Russell and Burch, 1959), there is universal agreement that animals should only be used for scientific purposes when no Replacement alternative is available. Where animals continue to be used, it is both a scientific and ethical imperative t...